Sigma & Pi Bonding

What are Sigma and Pi
bonds?

Many of us are already aware
of the definition of a sigma bond from our teachers, text books or from
many of the websites online. However, if you are still not aware of what these
two bonds are, then here is a basic definition of the two:

Sigma bond: A covalent bond resulting from the formation of a
molecular orbital by the end-to-end overlap of atomic orbitals, denoted by the
symbol σ.

Now have a look at this illustration to see how this end-to-end overlapping occures:

Fig 1: Formation of a Sigma bond

Misconception: many students in the Pacific may have this worng notion that a sigma

Pi bond: A covalent bond resulting from the formation of a
molecular orbital by side-to-side overlap of atomic orbitals along a plane perpendicular to a line connecting the nuclei of
the atoms, denoted by the symbol π.

Here's another illustration showing how the side-to-side overlapping occurs:

Fig 2: Formation of a Pi bond

It is important to note that
different sources use different terms to define what a sigma and pi bond is.
However, once examined carefully, it will be evident that they all try to
explain the same thing.

Misconception: many students in the Pacific may have this wrong notion that a sigma bond is the result of the overlapping of s orbitals and a pi bond is the result of the overlapping of p orbitals because they may relate the 's' to 'sigma' and the 'p' to 'pi'. However, it is seen that sigma bonds can be formed by the overlapping of both the s and p orbitals and not just s orbital.

You may have noticed that in order to understand these
definitions it is obvious that we must know what an s and p orbital is.

Note: A single bond such as (C-H)
has one sigma bond whereas a double (C=C) and triple (C≡C) bond has one sigma
bond with remaining being pi bonds.

Bond type

No. of σ bond

No. of π bonds

Single (C-H)

1

0

Double (C=C)

1

1

Triple (C≡C)

1

2

Sigma (σ) Bonding:

To understand Sigma bonding
let us look at the simple molecule of methane (CH4).

Methane, CH4

We may all be familiar with
drawing methane using electron dot diagrams, which would look something like
this:

Fig 3: Covalent bonding in Methane

Misconception: many students after drawing such electron dot diagrams fail to appreciate that in reality molecules exist as a 3D system and not as a two dimensional system as shown above. These diagrams are drawn for simplicity and should not be viewed as an exact representation of what a molecule looks like.

For
now, let us ignore the Hydrogen and concentrate on the central Carbon atom. We
know that it is the valence electrons that are responsible for covalent bonding
and we must know the electron configuration of an element from the periodic table to know how many
valence electron it has.

Now, when we look at the carbon
atom from our Methane, we see that its electron configuration is 1s2
2s2 2p2. However, from this electron configuration we can
see that carbon has only two unpaired electrons (2p2) in its valence
shell which can be used to form bonds with two hydrogen atoms. You can see this
more clearly in the electrons-in-boxes notation below.

Fig 3: Energy diagram for Carbon

So why is methane written as CH4
and not CH2? Well the answer to this lies in something know as hybridization.

Now that we have hybridized
the s and p orbitals of carbon to form four identical sp3 hybrid
orbitals, it is time to bring in the Hydrogens that we ignored earlier. It is
easy to see that the the four Hydrogens that will bond with the carbon all have
a single 1s orbital with a single unpaired electron in each. This makes it very
easy for it to bond with the carbon.

Fig 4: Sigma bonding in Methane. Source osxs.ch.liv.ac.uk

At
this point it is important that we notice how the 1s orbital of each of the
four hydrogen comes together with the sp3 orbital of the central
carbon. The two types of orbitals overlap in an end-to-end manner and form four
single bonds which are referred to as sigma bonds giving us our
methane molecule. Now remember the energy that the carbon atom gained to
promote one of its electrons from the 2s to the 2pz orbital during hybridisation? Well
once the carbon bonds with the hydrogens to form the CH4 molecule,
it loses far more energy compared to this gain which eventually makes the
molecule very stable and this is what is would look like:

Now
lets try to recap what we have learnt using the ethane C2H6
molecule.

First we isolate the two Carbons and get their
electron configuration which is 1s2 2s2
2p2

Since the electron configuration shows only two
unpaired electrons available for bonding and we know that each carbon can form
four bonds (3 bonds with hydrogen and 1 with the other carbon in this case), it
is obvious that hybridization is needed to make four unpaired electrons
available for this bonding.

Hybridization results in four sp3 hybrid
orbitals

Now three of these sp3 hybrid orbitals form
sigma bonds by overlapping with three 1s orbitals of the three hydrogens and the remaining sp3 hybrid orbital forms a sigma bond by overlapping with the sp3hybrid orbital of the other carbon which also has three Hydrogens bonded to it in the similar manner.

When all these sigma bonds have formed, we get a
molecule with a total of 7 sigma bonds. Have a look at the illustration of how the orbitals come together to form the bond and eventually the ethane molecule:

To understand pi bonding lets
have a look at the simple molecule of Ethene C2H4.

You may have drawn the ethane
molecule many times in your classrooms and we are all aware of how the atoms
and bonds are drawn to represent this molecule. Usually is would look something
like this:

Fig 7: Structure of Ethene

In
the case of Ethene, there is a difference from methane or ethane, because
each carbon is only joining to three other atoms rather than four. When the
carbon atoms hybridise their outer orbitals before forming bonds, this time
they only hybridise three of the orbitals rather than all four. They use
the 2s electron and two of the 2p electrons, but leave the other 2p electron
unchanged.

Fig 8: sp2 hybridisation

The new orbitals formed are called sp2
hybrids, because they are made by an s orbital and two p orbitals
which have reorganised themselves. sp2 orbitals look much like sp3
orbitals that you have already come across in the bonding in methane. The three
sp2 hybrid orbitals arrange themselves as far apart as possible,
which is at 120° relative to each other in a plane and remaining p orbital is at right
angles to them.

The two carbon atoms and four
hydrogen atoms would look like this before they joined together:

Fig 9: 1s and sp2
hybrid orbitals

The
various atomic orbitals which are pointing towards each other now merge to give
molecular orbitals, each containing a bonding pair of electrons. These are sigma
bonds - just like those formed by end-to-end overlap of atomic orbitals
that we saw in methane and ethane

The p orbitals on
each carbon aren't pointing towards each other, are overlapping sideways.

This sideways overlap also
creates a molecular orbital, but of a different kind. In this one the electrons
aren't held on the line between the two nuclei, but above and below the plane
of the molecule. A bond formed in this way is called a pi bond. Look at this illustration and notice how the orbitals have arranged themselves to form the pi bonds:

It is also important to note that this sort of overlapping
is represented by drawing a single line to show the bond. However this is just
for clarity and it does no mean that the electrons in a pi bond are present in
the same region as the electrons in the sigma bond as the structural diagram would suggest.

A pi bond would still have a pair of electrons. Many students may think that due to the orientation of the p orbitals that come together to form the pi bond, it would have four electrons (two above the plane and two below the plane) but this is not true.